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When printed at a uniform density (i.e. filled in, not hollow), this polyhedron has the property that it is only stable on one face. That is, it will always topple over an land on one side.
I have not had an opportunity to print them out, so I don't know if they work in practice. My understanding is that they are fairly sensitive to inaccuracies. I have provided a version of the polyhedron that is split in two, in the hope that it will print more accurately and can be glued together.
The existence of these polyhedra was first proven by Conway and Guy.
This particular one was taken from the mathematica notebook found at the article by Pegg, Ed Jr. and Weisstein, Eric W. "Unistable Polyhedron." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/UnistablePolyhedron.html
Unistable Polyhedron by jbrownkramer is licensed under the Creative Commons - Attribution license.
So what's this mean?
We're sure jbrownkramer would love to see what you've printed - take a photo and share it on Thingiverse as a Make.
To post a Make simply visit this Thing again and click I Made One to start uploading your photo. You can also download the Thingiverse Mobile app (available via Google Play and Apple App Store) to take a photo and upload your Make right from the app!